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The Problem of the Week Day 3: Week 6/19 - 6/25

Here is Day 3's problem. For the easy problem, you will only need yesterday's answers (keep Monday's for later though). For the hard problem, you will need Monday's and yesterday's answers. Good luck!

Easy Problem: If you have a number right next to an expression in parentheses, that also means multiplication. It's kind of like with a variable!

Plug z in from yesterday's work, and solve for n. [z(4 + z) + 5z]/(3z - 3) = n

Hard Problem: If you have two points on a linear graph, you can figure out it's slope (rate of change) by using the formula y2 - y1 / x2 - x1. So, if you had points (3, 0) and (4, 2), you would do 2 - 0 / 4 - 3 = 2 / 1 = 2. Therefore, 2 is your slope. Then, plug that into y = mx + b as m, and make b your y-intercept (where your line crosses the y axis). If you plug any point from the graph into that equation, it should be correct.

1) If yesterday's x = the x intercept of your graph (x , 0) and y = the y intercept of your graph (0 , y), find the slope (m) of this graph. What is this graph's equation?

m = ____

y = ____x + ____

2) Solve for r in the following equation: 1 + 8r^3 + 4^8 = (2b - a)^3 - 30 • 70 - 4 • 15

3) Plug r in for y in the graph's equation and find x. Since we already used x yesterday, we will call this value n.

n = ____

By the way, if you want to check in and see how you're doing, by all means, contact me at ethan@ethanmath.com. I will get back as soon as possible and tell you if you are correct.
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